A deterministic-stochastic method for computing the Boltzmann collision integral in \(\mathcal{O}(MN)\) operations

DOI10.3934/krm.2018047zbMath1405.76040OpenAlexW2803949462MaRDI QIDQ1715970

Erdal Karapınar

Publication date: 29 January 2019

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/krm.2018047

zbMATH Keywords

collision integralkinetic equationsconvolution formulationdynamics of non-continuum gasnodal-discontinuous Galerkin discretizations

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (3)

An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas ⋮ Implicit discontinuous Galerkin method for the Boltzmann equation ⋮ Fast evaluation of the Boltzmann collision operator using data driven reduced order models

Uses Software

• LAPACK
• PROPACK
• SMILE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
• A spectral-Lagrangian Boltzmann solver for a multi-energy level gas
• Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space
• A numerical model of the Boltzmann equation related to the discontinuous Galerkin method
• Vectorization of a Monte Carlo simulation scheme for nonequilibrium gas dynamics
• Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.
• Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
• Moment closure hierarchies for kinetic theories.
• A deterministic method for solving the Boltzmann equation with parallel computations
• Fast deterministic method of solving the Boltzmann equation for hard spheres
• On steady-state preserving spectral methods for homogeneous Boltzmann equations
• A Bhatnagar-Gross-Krook kinetic model with velocity-dependent collision frequency and corrected relaxation of moments
• A fast spectral method for the Boltzmann equation for monatomic gas mixtures
• A weak formulation of the Boltzmann equation based on the Fourier transform
• Method for solving the Boltzmann kinetic equation for polyatomic gases
• Solution of the Boltzmann equation for unsteady flows with shock waves in narrow channels
• Analysis of spectral methods for the homogeneous Boltzmann equation
• Shock and Boundary Structure Formation by Spectral-Lagrangian Methods for the Inhomogeneous Boltzmann Transport Equation
• A Fourier spectral method for homogeneous boltzmann equations
• Fast algorithms for computing the Boltzmann collision operator
• Solving the Boltzmann Equation in N log₂N
• Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation
• Origins of radiometric forces on a circular vane with a temperature gradient
• A Discrete Boltzmann Equation Based on a Cub-Octahedron in $\mathbb{R}^3$
• LAPACK Users' Guide
• A new consistent discrete-velocity model for the Boltzmann equation
• Efficient Deterministic Modelling of Three-Dimensional Rarefied Gas Flows
• Numerical methods for kinetic equations
• Convergence of A Distributional Monte Carlo Method for the Boltzmann Equation
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• Direct methods for solving the Boltzmann equation and study of nonequilibrium flows

This page was built for publication: A deterministic-stochastic method for computing the Boltzmann collision integral in \(\mathcal{O}(MN)\) operations